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Basics:
Dark Binding's (Q) damage is front loaded now, so its best to use it after Tormented Soil (W) has ticked a few times if possible to get maximum effect.
Tormented Soil at level 3 or 4 can clear an entire wave of ranged minions with ease.
Black Shield is very strong for initiating but I do not recommend getting it for the laning phase.
Soul Shackles does a ton of damage but you need to stay very close to enemies to finish the channel.

Build:
I usually go 9/21/0 masteries (http://www.fieldsofjustice.com/mastery/#/uZawZuPalawynwZy ) because most of morgana's spells you need to be very close to use effectively and getting a lot of tanky masteries allows you to lane much better. For runes I use Mpen marks, Mp5 per level seals, cooldown reduction per level glyphs, and flat hp quintessences. If you wanted to me more carry you can easily swap the cooldown glyphs for AP ones. For summoner spells I always take ghost and then either ignite or cleanse, depending on your team. If your team has a lot of squishy melee champions you will probably not be able to Black Shield yourself often so I would pick up Cleanse, otherwise you can be a lot more agressive with ignite.

Items:
Start with Doran's Ring and a Potion (if you're comfortably 2v2ing you can pick up a mana potion, otherwise if you're 2v1ing I'd grab a health potion)
First trip to base: Catalyst + basic boots.
2nd Trip to base: Rod of Ages and finish Mercury treads if possible.

Eventually you want something like this:
Doran's Ring
Rod of Ages
Mercury Treads
Zhonya's Ring
Rylais Crystalscepter
Will of the Ancients

If the enemy team has a lot of physical dps and your team is not very tanky you can substitute Sunfire capes in for will of the ancients and doran's ring.

Spells:
QWWQWRWEQQRQEEWREE

I start by maximizing my W first but you only need 4 ranks to be able to 1 shot ranged minion waves for most of the game. Q does a lot more damage to champions and scales much better otherwise. If the enemy team has a lot of CC you can level up E faster but at the cost of Q not W.

Strategy:
Farm as much as possible. I usually level W fastest at first to make it a lot easier to kill minion waves. If you position the tormented soil correctly you can hit the ranged minions and the melee ones and regenerate a ton of HP from her passive. Around level 3-4 of Tormented Soil you should be able to kill full health ranged minion waves with all of your passive Mpen and the shacking debuff from the spell itself.

Whenever possible try to move around the creep waves and push your opponents back. Like Ezreal, if your opponents move away from the creep waves to get away from you then they put themselves in an extremely difficult position to dodge.

Don't be afraid to ghost to keep Soul Shackles going. The amount of time it takes for the spell to explode and stun usually nets you enough time to get a Dark binding on them as well which will basically have killed any non-tank champion.

Although Morgana has very high AP ratios, if you don't have enough survival you will die very easily when trying to line up all of your spells. Focus on not dying first and let the spells do their magic.